Econ 2136

Lecture 1: Introduction

Edward Vytlacil

Yale University

Staff

  • Staff

  • Econometrics vs. Statistics/Data Science

  • Econ 2136

Professor: Edward Vytlacil

  • Economics Ph.d., Univeristy of Chicago,
    • studied under James Heckman.
  • Professor of Economics, Yale University,
    • previously on faculty at Stanford, Columbia, NYU.

Professor: Edward Vytlacil

Professor: Edward Vytlacil

Teaching Fellow: Wonwoo Bae

  • Yale Economics Ph.d. student.

  • Field: Econometric Theory

  • Contact:

Econometrics vs. Statistics/Data Science

  • Staff

  • Econometrics vs. Statistics/Data Science

  • Econ 2136

Course: Econ 2136, Econometrics

What is econometrics?

  • how is different from probability thoery? statistics?
    data science?

Probability theory

  • Branch of mathematics,
  • Derive implications of known probabilistic model.

Statistics builds upon prob. theory

  • “The science of learning from data”
    (estimation and inference of probabilistic model),
  • Origins in:
    • math/applied math,
    • experiments,
    • data scarcity.

Data Science

  • If statistics is the “science of learning from data,”
    then what is data science?

  • Is data science another name for applied statistics?

Data Science builds upon stats & CS

  • Data science origins in:
    • CS/engineering (not math),
    • environment of data abundance.
  • Data science overlaps with, but is different from stat:
    • different focus, perspective,

Data Science builds upon stats & CS

  • Data science different focus from stat, more focus on:
    • computation,
    • algorithms,
    • data visualization,
    • prediction,
    • domain expertise,
    • work flow…

Econometrics

  • Is econometrics the application of statistics to economic data? of data science to economic data?
  • No!!
    • Does not just apply statistics or data science .. .
    • Does not just consider “economic data.”

Econometrics

Samuelson, Koopmans, and Stone (1954):

the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference

  • For contemporary economics:
    • “economic phenomena” should be broadly construed,
    • econometrics sometimes tightly connected to econ theory, sometimes not.

Econometrics builds upon stats and econ theory

  • Merging of statistics, economic theory, and data
    (and more recently data science)
  • Econometrics origins in:
    • economic models,
    • not in experiments
      • though experimental analysis has become more important in economics/econometrics.

Econometrics builds upon stats and econ theory

  • Focus on counterfactual prediction,
    • sometimes answering “why” and often “what if”?
  • Different perspective on models and causality from stats.
    • ceterus paribus paradigm in economics,
    • though some partial convergence across fields.

Goals of econometrics include

  • Understanding economic phenomenon,
    • e.g., why did female labor force participation increase dramatically, especially in professional fields?

Goals of econometrics include

  • Distinguish correlation vs causality,
    • e.g., connection between access to birth control/abortion and female labor force participation?
    • answer “what if” questions.

Goals of econometrics include

Goals of econometrics include

  • Estimate economically meaningful quantities,
    • e.g., supply and demand functions, hedonic equations.
  • Test economic theory, inform economic theory,
    • e.g., distinguish taste-based vs statistical discrimination.

Influence of Econometrics

  • Econometrics grew out of econ, but has been influential in:
    • other social sciences
      (political science, law, …),
    • policy,
    • industry.
  • Has influenced statistics and CS/AI,
    • though relationship often contentious.

Econ 2136

  • Staff

  • Econometrics vs. Statistics/Data Science

  • Econ 2136

Econ 2136

  • Is designed for students in:

    • Economics & Mathematics joint major
    • Computer Science & Economics joint major.

  • Is designed to prepare students for graduate level courses.

  • Very different from Econ 1117/2123.

Econ 2136

  • Is an Econometrics course,
    • Considers empirical applications of interest to economists;
    • Teaches how economists think about data, connecting data to economic models.

Econ 2136

  • develops econometric theory,
    • develops theory with mathematical rigor, building upon theoretical statistics;
    • far more theoretical than the Econ 1117/2123 sequence;
    • appropriate training to prepare for graduate level courses.
    • why learn theory? why not just how to apply?

Econ 2136

  • develops econometric practice,
    • will develop when to use alternative econometric methods, how to justify their use, and interpret the results,
    • will use R to analyze real data of economic interest, including from recent economics publications.

Econ 2136

  • incorporates computationally intensive methods such as bootstrap and cross-validation,

  • incorporates aspects of data science.

Goal of Econ 2136

  • By the time you complete this course, for you to:
    • have a rigorous training in econometric theory, preparing you for future graduate-level work in econometrics or related fields;
    • have the strong basis for conducting original empirical research in economics, other social science, policy, or industry.

Math in Econ 2136

The course is substantially more mathematically rigorous than typical undergraduate-level econometrics courses, and will make extensive use of:

  • Multivariate calculus

  • Linear Algebra

Econ 2136: Textbooks

R in Econ 2136

  • The course will use more advanced coding than it typical for an undergraduate economics course, using R,
    • in R-Studio IDE, to

R in Econ 2136

  • create reproducible documents with R-Markdown/Quarto
    • combining text, code and results.

R in Econ 2136

  • In this course, we will use R,

    • what if you want to use STATA, python, . . .

  • Advantages of R over other options? Disadvantages?

Econ 2136 topics will include:

  • Conditional expectations and linear projections,

  • Causal Analysis,

  • Asymptotic Analysis,

  • Linear regression analysis, including model selection,

  • Bootstrap,

  • Instrumental Variables,

  • Limited Dependent Variable models.

Econ 2136 Applications include:

  • Finance:
    1. Asset diversification,
    2. Capital Asset Pricing Model,
  • Labor and education economics:
    1. Returns to schooling,
    2. Labor supply
    3. Effect of early childhood interventions.

Econ 2136 Applications include:

  • Discrimination, including in
    1. loans,
    2. job market,
    3. police force.

Will relate to economic models of discrimination:
statistical- vs taste-based discrimination.

Econ 2136: Prerequisites

  • Pre-Req:

    • Econ 2135: Introduction to Probability and Statistics, or
      S&DS 2410 and 2420.

    • What if you haven’t taken Econ 2135 or S&DS 2410+2420?

Econ 2136: Prerequisites

  • Math Pre-Req:
    • multivariate calculus as acquired by having already taken MATH 1200 or equivalent course,
    • linear algebra, as acquired by having already taken MATH 2250 or 2260 or equivalent course.

Lectures:

  • Lectures will primarily use blackboard, will sometimes be accompanying handouts.

  • We will sometimes live-code in R to analyze real data and to help you with your problem sets.

  • You are expected to attend lectures.
    I will call on students.

Course Webpages

Assignments Share of Course Grade
Online Quizzes 5%
Problem Sets 15%
Midterm 35%
Final 45%

On-Line Quizzes:

  • Posted on Fridays:
    • to the course webpage.
    • most weeks,
    • remain live for 48 hour once posted,
    • you have one hour to complete the quiz once you start it.
  • Quizzes will focus on theoretical questions, some questions on R coding.

On-Line Quizzes:

  • Open book/open notes,
    • but you cannot collaborate with, or discuss with, other students until the solutions are posted.
  • Lowest quiz score will be dropped.

Problem Sets

  • Will include primarily theoretical questions but also computational/empirical work.

  • Due dates are strict.1

  • The lowest problem set score will be dropped.

Problem Sets

  • You may work in groups of up to four students on the problem sets.1

  • However, you must turn in your own assignment and indicate on your submission the other members of the group.

Exams

  • Midterm:
    • in-class, Thursday February 26 (date tentative)
  • Final:
    • Tuesday, May 5, 2026 at 7pm.
  • Exams will focus on theory, with some R related questions including interpreting empirical output from R.

What’s next

What’s next

  • On Thursday, lecture will review rules for expected value and variance of random vectors.

    • Optional Reading: Review Expectations and Variance

What’s next

What’s next

What’s next

  • First quiz goes live Friday January 23.

  • First problem set due Thursday February 5 at 2:30pm.

    • Will include theoretical questions as well as use R.

References

Donoho, David. 2017. “50 Years of Data Science.” Journal of Computational and Graphical Statistics 26 (4): 745–66. https://doi.org/10.1080/10618600.2017.1384734.
Goldin, Claudia. 2006a. “The Quiet Revolution That Transformed Women’s Employment, Education, and Family.” National Bureau of Economic Research Cambridge, Mass., USA.
———. 2006b. “The Quiet Revolution That Transformed Women’s Employment, Education, and Family.” American Economic Review 96 (2): 1–21.
Hansen, Bruce. 2022a. Econometrics. Princeton University Press. https://press.princeton.edu/books/hardcover/9780691235899/econometrics.
———. 2022b. Probability and Statistics for Economists. Princeton University Press. https://press.princeton.edu/books/hardcover/9780691235943/probability-and-statistics-for-economists.
James, Gareth, Daniela Witten, Trevor Hastie, Robert Tibshirani, et al. 2013. An Introduction to Statistical Learning in r. Vol. 112. Springer. https://www.statlearning.com.
Samuelson, Paul A, Tjalling C Koopmans, and J RICHARD N Stone. 1954. “Report of the Evaluative Committee for Econometrica.” JSTOR.